Measuring method and measuring apparatus

ABSTRACT

A measuring arrangement includes forming first and second pairs of light beams each having a low frequency light beam and a high frequency light beam. Both pairs of light beams generate beat signals of the same frequency. The low frequency light beam of either pair and the high frequency of the other pair pass through a predetermined optical path to cause phase changes in the same direction. Beat signals are generated by superposing the first and second beam pair to provide measurement information on the phase changes.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a measuring method and apparatus andmore particularly, the present invention is suitable for use in opticalheterodyne interference arrangements, for example, a very smalldisplacement measuring apparatus, an alignment apparatus, a brazingregistration evaluation apparatus, a length measuring instrument, or anapparatus which measures a very small displacement of an object by usinga diffraction means, such as a diffraction grating.

2. Description of the Related Art

Hitherto, a heterodyne interference method capable of detectinginformation on the phase of light which is in a linear relationship withdisplacement by phase detection has been widely used for thehigh-precision measurement of a very small displacement. In theheterodyne interference method, measurements are performed in such a waythat interference fringes which change in relation to time and areformed by two light beams whose frequencies are slightly different fromeach other are photoelectrically detected, and the phase of theinterference fringes is converted into the phase of an electricalsignal.

FIG. 1 shows a conventional embodiment, which is a very smalldisplacement measuring apparatus which uses a Zeeman laser 301 for alight source and utilizes linearly polarized light beams 302 and 303intersecting at right angles with each other, frequencies thereof beingslightly different from each other, and which constitutes aninterferometer. The light 302 is P polarized light having a frequencyf₁, the electrical vector of which is light within the diagram. Thelight 303 is S polarized light having a frequency f₂, the electricalvector of which is light perpendicular to the diagram. Complex amplitudedisplays E₁ and E₂ of respective lights 302 and 303 emitted from theZeeman laser 301 can be expressed as follows when their respectiveinitial phases are denoted as φ₁ and φ₂ :

    E.sub.1 =A.sub.0 exp {i (w.sub.1 t+φ.sub.1)}           (1)

    E.sub.2 =B.sub.0 exp {i (w.sub.2 t+φ.sub.1)}           (2)

where A₀ and B₀ are amplitudes, w₁ and w₂ are angular frequencies, w₁=2π f₁ and w₂ =2π f₂. Lights 302 and 303 are each amplitude-divided by abeam splitter 304. Either one of light 302 or 303 becomes referencelight 306 or 307, and either one of light 302 or 303 becomes signallight 315 or 316 which enter an interferometer.

At this time, the polarization directions of the reference lights 306and 307 are aligned by a polarization plate 305 (a polarizer forextracting polarization components which are inclined by 45° in theirrespective polarization directions) and are detected by a photoelectricdetector 317. Complex amplitude displays E_(1R) (the complex amplitudeof light 307) and E_(2R) (the complex amplitude of reference light 306)of the reference light beams 307 and 306 at this time are as shown belowif L_(S) and L₀ denote respectively an optical path length from thelight source 301 to the beam splitter 304 and an optical path lengthfrom the beam splitter 304 to the photoelectric detector 317, as shownin FIG. 1, and A₁ and B₁ denote the respective amplitudes of thesedisplays E_(1R) and E_(2R) :

    E.sub.1R =A.sub.1 exp [i {(w.sub.1 t+φ.sub.1 -k.sub.1 (L.sub.S +L.sub.0)}]                                               (3)

    E.sub.2R =B.sub.1 exp [i {(w.sub.2 t+φ.sub.2 -k.sub.2 (L.sub.S +L.sub.0)}]                                               (4)

where k₁ and k₂ represent the number of waves. If c denotes a lightvelocity, the following relations are satisfied: ##EQU1## Thepolarization direction of the reference light beams 306 and 307 arealigned by the polarization plate 305 so that light beams 306 and 307interfere with each other. When this interference light isphotoelectrically detected by the photoelectric detector 317, adetection signal I_(R) is:

    I.sub.R =A.sup.2.sub.1 +B.sup.2.sub.1 +2A.sub.1 B.sub.1 COS {(w.sub.1 -w.sub.2) t+(φ.sub.1 -φ.sub.2)+(k.sub.2 -k.sub.1) (L.sub.S +L.sub.0)}                                                (5)

This detection signal is a beat signal having an angular frequency of w₁-w₂, i.e., a frequency of f₁ -f₂, and a phase of φ_(R) =(φ₁ -φ₂)+(k₂-k₁) (L_(S) +L₀). In contrast, light which is transmitted through thebeam splitter 304 enters a polarization beam splitter 308. Light beam315 of S polarization is reflected thereby, is reflected by a mirror310, and travels again toward the polarization beam splitter 308. Atthis time, the polarization direction is rotated by π/2 as a result ofthe light beam 315 passing two times through a λ/4 plate 309 disposed inthe optical path. Because the light has become light of P polarization,it is transmitted through the beam splitter 308. Light beam 316 of Ppolarization is transmitted through the polarization beam splitter 308and is reflected by an object 312 to be measured. The light beam 316travels again toward the polarization beam splitter 308. In the samemanner as described above, the polarization direction is rotated by π/2as a result of light beam 316 passing two times through a λ/4 plate 311disposed in this optical path. Because the light beam has become lightof S polarization, it is reflected by the polarization beam splitter308. Thereafter, the polarization directions of signal light beam 316 ofS polarization and signal light beam 315 of P (5) and (8) is measured byusing a lock-in amplifier 319 as a synchronization wave detector.

The difference Δφ between the phases of the beat signals shown inequations (5) and (8) is determined as shown in the following equation:

    Δφ=(k.sub.2 -k.sub.1) (L.sub.0 -L.sub.1)-2k.sub.1 ΔL.

By rearranging this, it follows that: ##EQU2## If Δφ₀ when ΔL=0 ismeasured beforehand, L₀ -L₁₌Δφ₀ /(k₂ -k₁). Since k₁ and k₂ are known, L₀-L₁ can be determined.

Thereafter, if the difference Δφ between the phases of the two beatsignals shown in equations (5) and (8) is measured, a displacement ΔL ofan object to be measured can be determined on the basis of equation (9).

However, the resolution of such a heterodyne interference measurementdepends upon the resolution of a phase measuring apparatus whichmeasures the phase difference between two beat signals. To increase themeasurement resolution, the resolution of a phase measuring apparatusmust be increased. However, there is a technical limitation regardingthis.

Hitherto, a so-called optical encoder which measures a movement amountor a rotation amount of an object by using an optical scale has beenused in the field of mechanical control. A conventional optical encoderhas been disclosed in, for example, Japanese Patent Laid-Open No.58-191907. In this optical encoder, coherent light from a light sourceis made to enter a diffraction grating which is a reference scalethrough a mirror or the like. ±N-th-order diffracted light emitted fromthis diffraction grating is reflected by a corner cube to its originaldirection and is also made to enter the diffraction grating. Then, twodiffracted light beams of ±N-th order are diffracted in the samedirection to interfere with each other. The intensity of the resultinginterference light is detected by an optical sensor.

Since such an apparatus is small and can achieve a high resolution, ithas been used for various purposes and for a variety of applications.

As machining and control have become more precise and fine, it has beenrequired that such a measuring apparatus have a higher resolution thanever before.

SUMMARY OF THE INVENTION

The present invention solves the above-mentioned problems in theabove-described conventional heterodyne interference measurement.

An object of the present invention is to provide a measuring method anda measuring apparatus capable of obtaining measurement accuracy twicethat attained by the prior art even if the resolution of the phasemeasuring apparatus is constant.

Another object of the present invention is to provide a measuringapparatus which achieves a higher resolution than before in the field ofoptical encoders in the optical displacement information detection.

The invention is directed to a measuring arrangement in which first andsecond pairs of light beams each having light beams of differentfrequencies are formed. A low frequency light beam of the first pair anda high frequency light beam of the second pair pass through apredetermined optical path so that the phases thereof are changed. Afirst beat signal is formed using the low frequency light beam of thefirst beam pair from the predetermined optical path and a second beatsignal is formed using the high frequency light beam of the second beampair from the predetermined optical path. The phase change informationis measured by comparing the first and second beat signals.

The method of preferred embodiments of the present invention whichachieves the above-described objects includes the steps of: forming afirst pair of beams having different frequencies and a second pair ofbeams having different frequencies, both pair of beams generating beatsignals having the same frequency; causing a light beam of one of thepair of beams having a low frequency and a light polarization arealigned by a polarization plate 314 similar to the polarization plate305 and detected by a photoelectric detector 318. If A₂ and B₂ denotetheir respective amplitudes, L₁ denotes the optical path length of thelight flux 315 from the beam splitter 304 to the photoelectric detector318 after it is reflected by a mirror 310, L₁ +2ΔL denotes the opticalpath length of the light flux 316 from the beam splitter 304 to thephotoelectric detector 318 after it is reflected by the object 312 to bemeasured, complex amplitude displays E_(1s) and E_(2s) of respectivelight beams 316 and 315 in the photoelectric detector 318 can beexpressed as follows:

    E.sub.1s =A.sub.2 ·exp [i {(w.sub.1 t+φ.sub.1 -k.sub.1 (L.sub.S +L.sub.1 +2ΔL)}]                           (6)

    E.sub.2s =B.sub.2 ·exp [i {(w.sub.2 t+φ.sub.2 -k.sub.2 (L.sub.S +L.sub.1)}]                                      (7)

The polarization directions of the signal light beam 315 and 316 arealigned by the polarization plate 314 to interfere with each other. Adetection signal I_(S) when the resulting interference light is detectedby the photoelectric detector 318 is:

    I.sub.s =A.sup.2.sub.2 +B.sup.2.sub.2 +2A.sub.2 B.sub.2 COS {(w.sub.1 -w.sub.2 ) t+(φ.sub.1 φ.sub.2)+(k.sub.2 -k.sub.1) (L.sub.S +L.sub.1)-2k.sub.1 ΔL}                              (8)

This detection signal is a beat signal having a frequency of w₁ -w₂,i.e., a frequency of f₁ -f₂, and a phase of φ_(S) =(φ₁ -φ₂)+(k₂ -k₁)(L_(S) +L₁)-2k₁ ΔL. The difference Δ(φ_(R) -φ_(S)) between the phases ofthe beat signals shown in equations beam of the other pair of beamshaving a high frequency to pass through a predetermined optical pathwhich causes the phase thereof to be changed in the same direction; andmeasuring information on the phase change by comparing the beat signalsgenerated when the first pair of beams and the second pair of beams aresuperposed.

The apparatus of preferred embodiments of the present invention whichachieves the above-described objects includes a light-beam former forforming a first pair of beams having different frequencies and a secondpair of beams having different frequencies, both pairs of beamsgenerating beat signals of the same frequency; an optical unit forsuperposing the first pair of beams and the second pair of beams after alight beam of one of the pair of beams having a low frequency and alight beam of the other pair of beams having a high frequency are causedto pass a predetermined optical path for causing the phase to be changedin the same direction; and a phase change information detector formeasuring information on the phase change by comparing the beat signalsgenerated when the first pair of beams and the second pair of beams aresuperposed.

Objectives and advantages in addition to those discussed above shall beapparent to those skilled in the art from the description of thepreferred embodiments of the invention which follow. In the description,reference is made to the accompanying drawings, which form a parthereof, and which illustrate an example of the invention. Such example,however, is not exhaustive of the various embodiments of the invention,and therefore reference is made to the appended claims for determiningthe scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view illustrating a very small displacement measuringapparatus of the prior art;

FIG. 2A is a view illustrating a first embodiment of the presentinvention;

FIG. 2B shows waveforms illustrating the principles of the presentinvention;

FIG. 3 is a view illustrating a second embodiment of the presentinvention;

FIG. 4 is a top plan view illustrating a diffraction grating accordingto the second embodiment;

FIG. 5 is a view illustrating a third embodiment of the presentinvention;

FIG. 6 is a view of the arrangement of a detection pattern (diffractiongrating) according to the third embodiment;

FIG. 7 is an enlarged view of an interference system according to thethird embodiment;

FIG. 8 is a view illustrating a fourth embodiment of the presentinvention;

FIG. 9 is a view illustrating the construction of a frequency shifteraccording to the fourth embodiment;

FIG. 10 is a view illustrating a fifth embodiment of the presentinvention;

FIG. 11 is a view illustrating a sixth and a seventh embodiment of thepresent invention;

FIG. 12 is a view illustrating an eighth embodiment of the presentinvention;

FIG. 13 is a view illustrating a ninth embodiment of the presentinvention;

FIG. 14 is a view illustrating a tenth embodiment of the presentinvention;

FIG. 15 is a schematic view of an apparatus using the technology whichis a prerequisite for subsequent embodiments of the present invention;

FIG. 16 is a schematic view of a length measuring apparatus of aneleventh embodiment of the present invention;

FIG. 17 is a schematic view of a length measuring apparatus of a twelfthembodiment of the present invention;

FIG. 18 is a schematic view of a length measuring apparatus of athirteenth embodiment of the present invention; and

FIG. 19 is a view illustrating the optical system of a part of thethirteenth embodiment of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

First, the principles of the embodiments of the present invention willbe explained.

Light beams from a light source section which emits a light beam f₁ anda light beam f₂ whose frequencies are slightly different from each otheris irradiated onto an object to be measured. The light beam f₁, which isreflected, diffracted, or scattered by the object to be measured, isinterfered with the light beam f₂, which does not need to be reflected,diffracted, or scattered by the object to be measured and which haspassed through a different optical path to form a first beat light beam.In the same manner as above, the light beam f₂, which is reflected,diffracted, or scattered by the object to be measured, is interferedwith the light beam f₁, which does not need to be reflected, diffracted,or scattered by the object to be measured and which has passed throughan optical path different from that passed through by the light beam f₂to form a second beat light beam. A measuring apparatus is constructedso that the signs of the phases of respective beat light beamscorresponding to a measured amount (e.g., a displacement amount) of anobject to be measured are different. These two beat light beams aredetected by different photoelectric detectors.

As a result of synchronously detecting two beat signals obtained in theabove-mentioned way with a synchronization detector, an object ismeasured on the basis of the detected phase difference.

The change of a beat signal over a period of time is shown in FIG. 2B.In the prior art, detection signals of a reference light beam are alwaysfixed, and no change in the phase occurs. This is made into a referencesignal 13 in FIG. 2B. In contrast, in the detection signals of a signallight beam, a phase change of Δφ₀ occurs according to the measuredamount. The phase difference between these two signals is measured as aphase difference of Δφ₀ by using a synchronization detector.

According to an embodiment of the present invention which will bedescribed later, detection signals of the first beat light beam aredesignated by reference numeral 14 and detection signals Δφ₁ of thesecond beat light beam are designated by reference numeral 14' in FIG.2B. Phase differences of Δφ₁ and Δφ₂ are caused respectively accordingto the measured amount. A measuring apparatus is constructed so that twobeat signals such that the signs of the phase changes Δφ₁ and Δφ₂ aredifferent can be obtained. If the apparatus is set so that Δφ₁ =Δφ₀ andΔφ₁ =-Δφ₀, and if the phase difference between the two signals ismeasured by using a synchronization detector, Δφ=Δφ₀ -(-Δφ₀)=2Δφ₀, aphase difference detected by the present measuring method is twice thatmeasured by the conventional method.

The embodiments will be explained below specifically with reference tothe accompanying drawings.

FIG. 2A shows the first embodiment of the present invention, which is avery small displacement measuring apparatus. Polarized light 2 (Ppolarized, frequency f₁) and polarized light 3 (S polarized, frequencyf₂) emitted from a Zeeman laser 1, which intersect at right angles witheach other, are amplitude-divided by a beam splitter 4. Light beams 2'and 3' (reflected light beams of light beams 2 and 3 respectively)reflected by the beam splitter 4 are transmitted through a λ/4 plate 5.After the light beams are reflected by a mirror 6, they are againtransmitted through the λ/4 plate 5 and reenter the beam splitter 4. Atthis time, the polarization direction is rotated by π/2 as a result ofthe light passing through a π/4 plate 5 twice. Light beam 2' becomes Spolarized light from P polarized light, and light beam 3' becomes Ppolarized light from S polarized light. Of the light which has reenteredand been transmitted through the beam splitter 4 (light which isreflected by the beam splitter 4 at this time is omitted in FIG. 2A), Ppolarized light 3' is transmitted through a beam splitter 9, and Spolarized light 2' is reflected thereby.

On the other hand, light beams 2" and 3" (transmitted light of lightbeams 2 and 3 respectively) which have been transmitted through the beamsplitter 4 after being emitted from the Zeeman laser 1, are reflected byan object 7 to be measured and enter the beam splitter 4 again.

Of the light (light which is transmitted through the beam splitter 4 atthis time is omitted in FIG. 2A) which has reentered the beam splitter 4and has been reflected thereby, p polarized light 2" is transmittedthrough the beam splitter 9, and S polarized light 3" is reflectedthereby.

Light beams 2" and 3' which are transmitted through the polarizationbeam splitter 9 and light beams 2' and 3" reflected thereby forminterference light beams because their polarization directions arealigned. These interference light beams are photoelectrically detectedby photoelectric detectors 10 and 11. The difference between the phasesof the signals obtained at that time is detected by using a lock-inamplifier 12a.

When the optical path length from the beam splitter 4 to the mirror 6and that from the beam splitter 4 to the object 7 to be measured areequal, and when the distance from the polarization beam splitter 9 tothe photoelectric detector 10 and that from the polarization beamsplitter 9 to the photoelectric detector 11 are equal, the optical pathlength from the Zeeman laser 1 to the photoelectric detector 10 is equalto that from the Zeeman laser 1 to the photoelectric detector 11. If theoptical path length at this time is denoted as L, a detection signalwhen the object 7 to be measured is displaced by ΔL in the X directionin this condition is as shown below. Complex amplitude displays E_(p)(f₁) and E_(p) (f₂) of light transmitted through the polarization beamsplitter 9, in the photoreceptor portion of the photoelectric detector10, can be expressed respectively as follows:

    E.sub.p (f.sub.1)=A exp [i {(w.sub.1 t+φ.sub.1 -k.sub.1 (L.sub.1 +2ΔL)}]                                             (1)

    E.sub.p (f.sub.2)=B exp [i {(w.sub.2 t+φ.sub.2 -k.sub.2 L)}](11)

where A and B are amplitudes, w₁ and w₂ are angular frequencies, w₁ =2πf₁ and w₂ =2π f₂, φ₁ and φ₂ are the initial phases of light emitted fromthe Zeeman laser 1, and k₁ and k₂ are the number of waves. If c denotesa light flux, the following relations are satisfied: ##EQU3## E_(p) (f₁)and E_(p) (f₂) interfere with each other because their polarizationdirections are aligned. A detection signal I₁ when this resultinginterference light is photoelectrically detected by the photoelectricdetector 10 is:

    I.sub.1 =A.sup.2 +B.sup.2 +2AB COS {(w.sub.1 -w.sub.2) t+(φ.sub.1 -φ.sub.2)-2k.sub.1 ΔL}                          (12)

On the other hand, complex amplitude displays E_(s) (f₁) and E_(s) (f₂)of light beams which are reflected by the polarization beam splitter 9,in the photoreceptor portion of the photoelectric detector 11, can beexpressed respectively as follows:

    E.sub.s (f.sub.1)=A exp [i {(w.sub.1 t+φ.sub.1 -k.sub.1 L)}](13)

    E.sub.s (f.sub.2)=B exp [i {(w.sub.2 t+φ.sub.2 k.sub.2 (L+2ΔL))}](14)

Since the polarization directions of E_(s) (f₁) and E_(s) (f₂) arealigned, they interfere with each other, A detection signal I₂ when thisresulting interference light is photoelectrically detected by thephotoelectric detector 11 is:

    I.sub.2 =A.sup.2 +B.sup.2 +2AB COS {(w.sub.1 -w.sub.2) t+(φ.sub.1 -φ.sub.2)+2k.sub.2 ΔL}                          (15)

A phase difference Δφ' between the phase of I₂ and that of I₁ can bedetermined as follows with the photoelectrically detected signals I₁ andI₂ as the two input signals to a lock-in amplifier 12a:

    Δφ'=2 (k.sub.1 +k.sub.2) ΔL                (16)

Δφ' changes by 2 (k₁ +k₂) ΔL relative to the displacement ΔL of theobject 7 to be measured.

By rearranging equation (16), it follows that: ##EQU4## Thus, adisplacement X can be determined by measuring the phase difference Δφ'between the beat signals. According to this method, a sensitivity about(k₁ +k₂)/k₁ times, or twice that of the prior art, can be obtained withrespect to the displacement of an object to be measured because k₁ ≈k₂.That is, when a lock-in amplifier having the same accuracy is used, anaccuracy twice that of the prior art can be obtained. The output of thelock-in amplifier 12a is input to an computing unit 12b, whereby ΔL ismeasured on the basis of the rearranged equation of equation (16).

FIG. 3 is a view illustrating the second embodiment of the presentinvention and shows the alignment section of a proximity exposure typesemiconductor manufacturing apparatus which uses far-infrared rays, Xrays or the like. The alignment of a mask 22 with a wafer 23 isperformed by using an alignment mark 24 formed of a diffraction gratingdisposed on the mask 22 and an alignment mark 25 formed of a diffractiongrating disposed on the mask 23. Polarized light beam 16 (P polarized,frequency f₁) and polarized light beam 17 (S polarized, frequency f₂)emitted from a Zeeman laser 15, which intersect at right angles witheach other, are amplitude-divided by a beam splitter 18. Light beams 16'and 17' (reflected light beams of light beams 16 and 17 respectively)reflected by the beam splitter 18 are transmitted through a λ/2 plate19. At this time, the polarization direction is rotated by π/2. Lightbeam 16' becomes an S polarized light beam 16'" (frequency f₁) from Ppolarized light, and light beam 17' becomes a P polarized light beam17'" (frequency f₂) from S polarized light. Light beams 16'" and 17'"which have been transmitted through the λ/2 plate 19 change theircourses by means of a mirror 20, and are irradiated onto both thediffraction grating 24 disposed on the mask 22 and the diffractiongrating 25 disposed on the wafer 23.

In contrast, light beams 16" and 17" which have been transmitted throughthe beam splitter 18 (transmitted light beams of light beams 16 and 17,respectively) change their courses by means of a mirror 21, and areirradiated onto the diffraction grating 24 and the diffraction grating25.

The diffraction gratings 24 and 25 are reflection type evenly-spacedlinear diffraction gratings. Their pitches are equal, the value being P.FIG. 4 shows the arrangement of the alignment marks 24 and 25, seen fromthe direction of the normal line of the mask 22 and the wafer 23, andirradiated light. Of the light diffracted by the diffraction grating,the diffracted light to the left side (the -x side), when the X-Z planeon the figure toward the traveling direction of the 0-th orderdiffracted light (regularly reflected light) is seen from the +y side,is made into +m-th diffracted light, whereas light diffracted 25 to theright side (+x side) is made into -m-th order diffracted light. It isgenerally well known that, when a diffraction grating moves one pitch ina direction (the +x-axis direction in FIG. 3) perpendicular to thegrating patterns of the diffraction grating, the phase of the diffractedlight changes by 2 mπ. When the diffraction grating 24 is moved by x_(M)in a x direction from a reference position, and when the diffractiongrating 25 is moved by x_(W) in a x direction from a reference position,a phase change of ±2mπx_(M) /P±2mπx_(W) /P is applied to the lightdiffracted by each diffraction grating. The incident angles of±first-order diffracted light used for measurements from the diffractiongratings 24 and 25 are set so that they are diffracted in the directionof the normal line of the diffraction grating 24 and that of thediffraction grating 25. Light diffracted in the direction of the normalline will be considered.

Complex amplitude displays E_(MS) (f₁) and E_(MP) (f₂) of +first-orderdiffracted light of the left-side incident light 16'" and 17'" by meansof the diffraction grating 24, and complex amplitude displays E_(MP)(f₁) and E_(MS) (f₂) of -first-order diffracted light of the right-sideincident light 16' and 17' are as shown in the following equations:

    E.sub.MS (f.sub.1)=A exp {i (w.sub.1 t+φ.sub.1 +φ.sub.M)}(17)

    E.sub.MS (f.sub.2)=B exp {i (w.sub.2 t+φ.sub.2 +φ.sub.M)}(18)

    E.sub.MP (f.sub.1)=A exp {i (w.sub.1 t+φ.sub.1 -φ.sub.M)}(19)

    E.sub.MP (f.sub.2)=B exp {i (w.sub.2 t+φ.sub.2 -φ.sub.M)}(20)

where A and B are amplitudes, w₁ and w₂ are angular frequencies, φ₁ andφ₂ are the initial phases of light emitted from the Zeeman laser 15, andφ_(M) =2πx_(M) /P. In the same manner as above, complex amplitudedisplays E_(WS) (f₁) and E_(WP) (f₂) of the +first-order diffractedlight beams of the left-side incident light beams 16'" and 17'" by meansof the diffraction grating 25, and complex amplitude displays E_(WP)(f₁) and E_(WS) (f₂) of the -first-order diffracted light beams of theright-side incident light beams 16" and 17" are as shown in thefollowing equations:

    E.sub.WS (f.sub.1)=A exp {i (w.sub.1 t+φ.sub.1 +φ.sub.W)}(21)

    E.sub.WP (f.sub.2)=B exp {i (w.sub.2 t+φ.sub.2 +φ.sub.W)}(22)

    E.sub.WP (f.sub.1)=A exp {i (w.sub.1 t+φ.sub.1 -φ.sub.W)}(23)

    E.sub.WS (f.sub.2)=B exp {i (w.sub.2 t+φ.sub.2 -φ.sub.W)}(24)

where φ_(w) =2πX_(W) /P.

Those light beams in which polarization planes of the light beamsdiffracted by the diffraction gratings 24 and 25 are aligned, interferewith each other, and four interference light beams are obtained. Of thelight beams diffracted by the diffraction grating 24, P polarized lightbeams are expressed by equations (18) and (19). The intensity changeI_(MP) of an interference light 36 is:

    I.sub.MP =A.sup.2 +B.sup.2 +2AB cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)-2φ.sub.M }                              (25)

In the same manner as above, S polarized light beams are expressed byequations (17) and (20). The intensity change I_(MS) of an interferencelight beam 37, intensity changes I_(WP) and I_(WS) of an interferencelight beam 38 of P polarization of equations (22) and (23), and of aninterference light beam 39 of S polarization of equations (21) and (24),can be expressed by the following equations:

    I.sub.MS =A.sup.2 +B.sup.2 +2AB cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)-2φ.sub.M }                              (26)

    I.sub.WP =A.sup.2 +B.sup.2 +2AB cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)+2φ.sub.W }                              (27)

    I.sub.WS =A.sup.2 +B.sup.2 +2AB cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)-2φ.sub.W }                              (28)

These four interference light beams are detected independently of eachother by photoelectric detectors 30, 33, 31 and 32.

The respective interference light beams may be separated as described inthe examples below.

The direction of the light diffracted by the diffraction gratings 24 and25 is changed by a mirror 26 and guided to a polarization beam splitter27. As a result, P polarized interference light beams 36 and 38 aretransmitted therethrough and S polarized interference light beams 37 and39 are reflected thereby, the beams being divided into two.

The edge mirrors 28 and 29 are arranged in such a way that outgoinglight from near a diffraction grating is spatially separated by aboundary line 40 shown in FIG. 4, seen from the plane where thediffraction grating exists. This arrangement causes the interferencelight beams 36 and 37 of the light diffracted by the diffraction grating24 and the interference light beams 36 and 37 of the light diffracted bythe diffraction grating 25 to be divided into two. Respectiveinterference light beams separated in this manner are converted intoelectrical signals by the photoelectric detectors 30, 31, 32 and 33(e.g., avalanche photodiodes) and guided to lock-in amplifiers 34 and35. When a phase deviation ΔT_(M) between the beat signals having afrequency of w₁ -w₂, caused by the light beams 36 and 37 diffracted bythe diffraction grating 24, shown in equations (25) and (26), isdetected by using the lock-in amplifier 35, it is expressed as follows:##EQU5## The amount of deviation X_(M) of the mask 22 along the xorientation is determined by detecting the phase with the lock-inamplifier 35. In similar manner, a phase deviation ΔT_(W) between thesignals shown in equations (27) and (28) is detected by using thelock-in amplifier 34, it is expressed as follows: ##EQU6## Thus, theamount Of the deviation X_(W) of the wafer 23 along the x orientationcan be determined. The mask 22 can be aligned with the wafer 23 bycausing the wafer to move so that the amounts of the deviation of themask 22 and the wafer 23 along the x orientation are equal.

If the pitches of the diffraction gratings 24 and 25 are set at 2 μm;the central wavelength of light emitted from the Zeeman laser 15 is setat λ=0.6328 μm; and the diffraction angle of ±first-order diffractedlight when light is incident perpendicularly to the diffraction gratings24 and 25 is denoted as θ±1, then θ±1=sin⁻¹ (0.6328/2)=18.4° on thebasis of the relation of:

    θ±m=sin (mλ/P) (m=order of diffraction)    (29)

Therefore, to cause light incident on the diffraction gratings 24 and 25to be diffracted upward perpendicularly to the mask 22 and the wafer 23,the mirrors 20 and 21 should be set so that the right and left incidentangles are equal to θ±1.

The determination of the amount of the deviation of the diffractiongrating 24 on the mask 22 and of the diffraction grating 25 on the wafer23, on the basis of the above-described principles, enables thealignment of a semiconductor exposure apparatus to be preciselydetected. In this way, in this embodiment, two light beams havingdifferent frequencies (f₁ and f₂) which form beat signals are madeincident so that they are arranged opposite to each other with respectto the direction (along the x orientation) in which a positionaldeviation should be detected. Detection of position is performed on thebasis of the phase deviation between the beat signals formed by eachpair of two pairs of light beams. Therefore, when the detection ofposition performed on the basis of the phase deviation of beat signalsformed by one of the pairs of light beams of these two pairs of lightbeams is compared with the detection of position performed from thephase deviation of beat signals whose phase is fixed, the phasedeviation is twice the amount of positional deviation. Therefore theposition deviation detection resolution is increased two-fold.

Outputs from the lock-in amplifiers 34 and 35 are sent to a centralcontrol unit C_(P), whereby the amount of deviation of the mask from thewafer is detected (or the presence and direction of the deviation). Inresponse to the deviation detection, a drive command signal is issued toat least either one of a well-known mask actuator 22A for driving a maskin the x direction and a well-known wafer actuator 23A for driving awafer in the x direction, and the mask is aligned with the wafer. Oneset of these actuators is disposed along the y orientation, andalignment along the y orientation is performed in similar fashion asthat along the x orientation, though this has been omitted in theexplanation.

FIG. 5 illustrates the third embodiment of the present invention andshows a brazing superposition evaluation apparatus for preciselydetecting and evaluating the deviation of positions between two brazingsuperposition evaluation patterns brazed by two exposures. Polarizedlight 42 (P polarized, frequency f₁) and polarized light 43 (Spolarized, frequency f₂) emitted from a Zeeman laser 41, which intersectat right angles with each other, are amplitude-divided by a beamsplitter 44. Light beams 42' and 43' (the reflected light beams of lightbeams 42 and 43 respectively) reflected by the beam splitter 44 aretransmitted through a λ/4 plate 45. At this time, the polarizationdirection is rotated by π/2. Light beam 42' becomes an S-polarized lightbeam 42'" from P polarized light beam, and light beam 43' becomes aP-polarized light beam 43'" from S polarized light. The course of thelight beams 42'" and 43'" which have been transmitted through the λ/4plate 45 is deflected by a mirror 46 and the light beams are irradiatedonto the entire surface of diffraction gratings 48 and 49 disposed on awafer 50. The diffraction gratings 48 and 49 disposed on the wafer 50are two adjacent evenly-spaced linear diffraction gratings, shown inFIG. 6, formed on a wafer through several brazing processes. Theirpitches are equal, being P. A deviation Δx in position during brazing iscaused along the x orientation between the diffraction gratings 48 and49.

On the other hand, the course of light beams 42" and 43" (transmittedlight beams of the light beams 42 and 43) is changed by a mirror 47, andthe light beams are irradiated onto the diffraction gratings 48 and 49.At this time, complex amplitude displays E_(AS) (f₁) and E_(AP) (f₂) of+first-order diffracted light of the left-side incident light 42'" and43'" by means of the diffraction grating 48, and complex amplitudedisplays E_(AP) (f₁) and E_(AS) (f₂) of -first-order diffracted light ofthe right-side incident light 42" and 43" are as shown in the followingequations:

    E.sub.AS (f.sub.1)=A exp {i (w.sub.1 t+φ.sub.1 +φ.sub.A)}(30)

    E.sub.AP (f.sub.2)=B exp {i (w.sub.2 t+φ.sub.2 +φ.sub.A)}(31)

    E.sub.AP (f.sub.1)=A exp {i (w.sub.1 t+φ.sub.1 -φ.sub.A)}(32)

    E.sub.AS (f.sub.2)=B exp {i (w.sub.2 t+φ.sub.2 -φ.sub.A)}(33)

where A and B are amplitudes, w₁ and w₂ are angular frequencies, φ₁ andφ₂ are the initial phases of light emitted from the Zeeman laser 41, andφ_(A) =2πx_(A) /P. Also, respective complex amplitude displays E_(BS)(f₁) and E_(BP) (f₂) of -first-order diffracted light of the left-sideincident light 42'" and 43'" by means of the diffraction grating 49, andcomplex amplitude displays E_(BP) (f₁) and E_(BS) (f₂) of +first orderdiffracted light of the right-side incident light 42" and 43" are asshown in the following equations:

    E.sub.BS (f.sub.1)=A exp {i (w.sub.1 t+φ.sub.1 +φ.sub.B)}(34)

    E.sub.BP (f.sub.2)=B exp {i (w.sub.2 t+φ.sub.2 +φ.sub.B)}(35)

    E.sub.BP (f.sub.1)=A exp {i (w.sub.1 t+φ.sub.1 -φ.sub.B)}(36)

    E.sub.BS (f.sub.2)=B exp {i (w.sub.2 t+φ.sub.2 -φ.sub.B)}(37)

where φ_(B) =2πx_(B) /P. In the above equations, x_(A) and x_(B) denotethe amount of deviation of the diffraction gratings 48 and 49 from areference position in the x direction, respectively.

Those light beams in which polarization planes of the light beamsdiffracted by the diffraction gratings 48 and 49 are aligned, interferewith each other, and four interference light beams are obtained. Of thelight beams diffracted by the diffraction grating 48, P polarized lightbeams are expressed by equations (31) and (32). The intensity changeI_(AP) of an interference light 61 is:

    I.sub.AP =A.sup.2 +B.sup.2 +2AB cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)-2φ.sub.A }                              (38)

In similar manner, S polarized light beams are expressed by equations(30) and (33). The intensity change I_(AS) of an interference light beam62, intensity changes I_(BP) and I_(BS) of an interference light beam 63of P polarization of equations (35) and (36), and of an interferencelight beam 64 of S polarization of equations (39) and (37), can beexpressed by the following equations:

    I.sub.AS =A.sup.2 +B.sup.2 +2AB cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)-2φ.sub.A }                              (39)

    I.sub.BP =A.sup.2 +B.sup.2 +2AB cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)+2φ.sub.B }                              (40)

    I.sub.BS =A.sup.2 +B.sup.2 +2AB cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)-2φ.sub.B }                              (41)

These interference light beams are separated and photoelectricallydetected in order to detect beat signals of an angular frequency of w₂-w₁. The respective interference light beams may be separated as shownbelow. The state of the separation of the interference light beams isshown in FIG. 7. The direction of the light beam diffracted by thediffraction gratings 48 and 49 is changed by a mirror 51 and guided to apolarization beam splitter 52. As a result, the interference light beams61 and 63 of P polarization are transmitted through it, and theinterference light beams 62 and 64 of S polarization are reflected byit, being divided into two.

The interference light beams 61 and 63 of light beams each diffracted bythe diffraction gratings 48 and 49 respectively are divided into two byan edge mirror 53. The interference light beams 62 and 64 of light beamseach diffracted by the diffraction gratings 48 and 49 respectively aredivided into two by an edge mirror 54. Respective interference lightbeams are converted into electrical signals by photoelectric detectors55, 56, 57 and 58 and guided to lock-in amplifiers 59 and 60. When theamount of the phase deviation ΔT_(A) between the signals shown inequations (38) and (39) is detected by using the lock-in amplifier 60,it is expressed as follows: ##EQU7## Thus, the deviation X_(A) of thediffraction grating 48 along the x orientation is determined on thebasis of the phase of the output of the lock-in amplifier 60. In similarmanner, when a phase deviation ΔT_(B) between the signals shown inequations (40) and (41) is detected, it is expressed as follows:##EQU8## Thus, the deviation X_(B) of the diffraction grating 49 alongthe x orientation can be determined. Furthermore, the relative deviationAx between the diffraction gratings 48 and 49 can be determined by acomputing unit 65 that computes the difference between the X_(A) andX_(B) on the basis of the outputs of the lock-in amplifiers 59 and 60.In this embodiment, the phase deviation of beat signals with respect toa predetermined deviation amount is twice that when a phase differenceis determined with the beat signals whose phase is fixed as a reference.

Brazing superposition evaluation by a semiconductor exposure apparatuscan be performed by determining the deviation between a first brazedgrating pattern and a second brazed grating pattern on the basis of theabove-described principles. Grating patterns are brazed, for example, byeach of two exposures with a predetermined stage movement performed.Then, the above-described brazing superposition evaluation is performed.Thus, stage evaluation of the exposure apparatus can be made. Inaddition, after the first brazing is performed, alignment is performed.After a second exposure brazing, if the above-described superpositionevaluation is performed, alignment can be evaluated.

FIG. 8 illustrates the fourth embodiment of the present invention andshows a superposition measuring apparatus of a semiconductor exposureapparatus. In the third embodiment shown in FIG. 5, a case in which,light beams emitted from the Zeeman laser 41 are amplitude-divided by abeam splitter 44 and irradiated onto the diffraction gratings 48 and 49on the wafer 50, has been described. However, in this embodiment shownin FIG. 8, light beams emitted from a light source 70, such as a laser,are made into light beams u₁ (P polarization, frequency f₁) and u₂ (Spolarization, frequency f₂) whose frequencies f are slightly differentfrom each other and which intersect at right angles with each other, bymeans of a frequency shifter 71. Complex amplitude displays ofrespective light beams u₁ and u₂ are as shown in the equations showbelow if φ₁ and φ₂ denote the initial phases, C₁₀ and C₂₀ denoteamplitudes, w₁ and w₂ denote angular frequencies, and w₁ =2π f₁ and w₂=2πf₂ :

    u.sub.1 =C.sub.10 exp }i (w.sub.1 t+φ.sub.1)}          (42)

    u.sub.2 =C.sub.20 exp }i (w.sub.2 t+φ.sub.2)}          (43)

The diameters of the two light beams u₁ and u₂, on a common opticalpath, are condensed by a beam expander 72. The direction of travel ofthe light beams is changed by a mirror 73 and made to perpendicularlyenter a linear diffraction grating 74 (gratings are arrayed in thedirection from left to right in the diagram, and grating patterns extendin a direction perpendicular to the diagram). In the case of atransmission-type diffraction grating, diffracted light on the rightside (the +x side) with respect to the direction of the traveling of0-th order diffracted light (positive reflected light), when the x-zplane on the diagram of FIG. 8 is seen from the +y side, is made into+m-th order diffracted light. Diffracted light on the left side (the -xside) is made into -m-th order diffracted light. In the case of areflection-type diffraction grating, the reverse applies. Generally,when a diffraction grating is moved one pitch perpendicularly to thegrating pattern of the diffraction grating (the x orientation in FIG.8), the phase of the diffracted light changes by 2 mπ with m as theorder of diffraction. Therefore, when the diffraction grating 74 ismoved by x_(A) along the x orientation from a reference position, phasesof -2πx_(A) /P and 2πx_(A) /P are applied to first-order diffractedlight beams 76 and 77 (diffracted light beams of u₁ and u₂,respectively) and -first-order diffracted light 78 and 79 (diffractedlight beams of u₁ and u₂, respectively) where the pitch of thediffraction grating 74 as P. Complex amplitudes u₁ (1), u₂ (1), u₁ (-1)and u₂ (-1) (parentheses denote the order of diffraction) of±first-order diffracted light beams 76, 77, 78 and 79 from thediffraction grating are expressed as follows if C₁₁ and C₂₁ denoteamplitudes:

    u.sub.1 (1)=C.sub.11 exp {i (w.sub.1 t+φ.sub.1 +φ.sub.A)}(44)

    u.sub.2 (1)=C.sub.21 exp {i (w.sub.2 t+φ.sub.2 +φ.sub.A)}(45)

    u.sub.1 (-1)=C.sub.11 exp {i (w.sub.1 t+φ.sub.1 -φ.sub.A)}(46)

    u.sub.2 (-1)=C.sub.21 exp {i (w.sub.2 t+φ.sub.2 -φ.sub.A)}(47)

where φ_(A) =2πX_(A) /P.

A 0-th order diffracted light 80 is removed, for example, by a spacefilter 81 so that it cannot enter the diffraction gratings 48 and 49 onthe wafer 50. The first-order diffracted light beams 76 and 77 becomelight beams 76' and 77' in which their respective polarization planesare rotated by 90° by a 1/2 wavelength plate 75. The courses of thediffracted light beams 76' and 77', and 78 and 79 are changed by mirrors91 and 92, respectively, and the beams are irradiated onto the entiresurface of the diffraction gratings 48 and 49 disposed on the wafer 50.

The diffraction gratings 48 and 49 disposed on the wafer 50 are twoadjacent evenly-spaced linear diffraction gratings shown in FIG. 6, asin the third embodiment. Their pitches are equal, being P. A deviationΔx is caused along the x orientation between the diffraction gratings 48and 49.

At this time, first-order diffracted light beams u_(1B) (1, 1) andu_(2B) (1, 1) of light beams 76' and 77' diffracted by the diffractiongrating 48, and -first-order diffracted light beams u_(1B) (-1, -1) andu_(2B) (-1, -1) of light beams 78 and 79, are expressed as follows:

    u.sub.1B (1, 1)=C.sub.1B exp {i (w.sub.1 t+φ.sub.1 +φ.sub.A +φ.sub.B)}                                            (48)

    u.sub.2B (1, 1)=C.sub.2B exp {i (w.sub.2 t+φ.sub.2 +φ.sub.A +φ.sub.B)}                                            (49)

    u.sub.1B (-1, -1)=C.sub.1B exp {i (w.sub.1 t+φ.sub.1 -φ.sub.A -φ.sub.B)}                                            (50)

    u.sub.2B (-1, -1)=C.sub.2B exp {i (w.sub.2 t+φ.sub.2 -φ.sub.A -φ.sub.B)}                                            (51)

where C_(1B) and C_(2B) are amplitudes, and φ_(B) =2πX_(B) /P. Also,first-order diffracted light beams u_(1C) (1, 1) and u_(2C) (1, 1) oflight beams 76' and 77' diffracted by the diffraction grating 48, and-first-order diffracted light beams u_(1C) (-1, -1) and u_(2C) (-1, -1)of light beams 78 and 79, are expressed as follows:

    u.sub.1C (1, 1)=C.sub.1C exp {i (w.sub.1 t+φ.sub.1 +φ.sub.A +φ.sub.C)}                                            (48)

    u.sub.2C (1, 1)=C.sub.2C exp {i (w.sub.2 t+φ.sub.2 +φ.sub.A +φ.sub.C)}                                            (49)

    u.sub.1C (-1, -1)=C.sub.1C exp {i (w.sub.1 t+φ.sub.1 -φ.sub.A -φ.sub.C)}                                            (50)

    u.sub.2C (-1, -1)=C.sub.2C exp {i (w.sub.2 t+φ.sub.2 -φ.sub.A -φ.sub.C)}                                            (51)

where C_(1C) and C_(2C) are amplitudes, and φ_(C) =2πX_(C) /P. In theabove equations, X_(B) and X_(C) denote the deviation of the diffractiongratings 48 and 49 along the x orientation from the same referenceposition, respectively.

Those light beams in which polarization planes of the light beamsdiffracted by the diffraction gratings 48 and 49 are aligned, interferewith each other, and four interference light beams are obtained. Of thelight beams diffracted by the diffraction grating 48, P polarized lightbeams are expressed by equations (49) and (50). The intensity changeV_(BP) of the resulting interference light beam 107 is:

    V.sub.BP =C.sup.2.sub.1B +C.sup.2.sub.2B +2C.sub.1B C.sub.2B COS {(w.sub.2 -w.sub.1)+(φ.sub.2 -φ.sub.1)+2(φ.sub.B +φ.sub.A)}(56)

In similar manner, S polarized light beams are expressed by equations(48) and (51). The intensity change V_(BS) of the resulting interferencelight beam 108, intensity changes V_(CP) and V_(CS) of an interferencelight beam 109 of P polarization of equations (53) and (54), and of aninterference light beam 110 of S polarization of equations (52) and (55)of the light beams diffracted by the diffraction grating 49, can beexpressed by the following equations:

    V.sub.BS =C.sup.2.sub.1B +C.sup.2.sub.2B +2C.sub.1B C.sub.2B cos {(w.sub.2 -w.sub.1)+(φ.sub.2 -φ.sub.1)+2(φ.sub.B +φ.sub.A)}(57)

    V.sub.CP =C.sup.2.sub.1C +C.sup.2.sub.2C +2C.sub.1C C.sub.2C cos {(w.sub.2 -w.sub.1)+(φ.sub.2 -φ.sub.1)+2(φ.sub.C +φ.sub.A)}(58)

    V.sub.CS =C.sup.2.sub.1C +C.sup.2.sub.2C +2C.sub.1C C.sub.2C cos {(w.sub.2 -w.sub.1)+(φ.sub.2 -φ.sub.1)+2(φ.sub.C +φ.sub.A)}(59)

The respective interference light beams may be separated as described inthe examples below.

The course of the light beam diffracted by the diffraction gratings 48and 49 is changed by a mirror 96, and guided to a polarization beamsplitter 97. As a result, interference light beams 107 and 109 of Ppolarization are transmitted through the polarization beam splitter 97,and interference light beams 108 and 110 are reflected thereby, thebeams being divided into two. In addition, the light beams are dividedinto the following two beams by mirrors 98 and 99: (a) interferencelight beams 107 and 108 of light diffracted by the diffraction grating48, and (b) interference light beams 109 and 110 of light diffracted bythe diffraction grating 49. Respective interference light beamsseparated in this manner are converted into electrical signals by thephotoelectric detectors 100, 101, 102 and 103 (e.g., avalanchephotodiodes) and guided to lock-in amplifiers 104 and 105.

In equations (56), (57), (58) and (59), C² _(1B) +C² _(2B), and C² _(1C)+C² _(2C) are DC components, 2C_(1B) C_(2B) and 2C_(1C) C_(2C) areamplitudes of the frequency of f₂ -f₂. Signals having beat frequencycomponents of f₂ -f₂ undergo the initial phase deviation of φ₂ -₁, andare phase-modulated over a period of time by deviation 2(φ_(B) +φ_(A)),-2(φ_(B) +φ_(A)) for the diffraction grating 74 of the diffractiongrating 48 in the case of equations (56) and (57), and by the deviation2(φ_(C) +φ_(A)), -2(φ_(C) +φ_(A)) for the diffraction grating 74 of thediffraction grating 49 in the case of equations (58) and (59).Therefore, if a deviation over a period of time between the two signalsis detected with one of the signals shown in equations (56) and (57) asa reference signal and the other as a signal to be measured, the initialphase of the light beam can be erased, making highly precise positiondetection possible in so-called heterodyne interference measurement.

As described above, since, in the heterodyne interference method, aphase deviation between two signals is detected as time and not affectedby a difference between DC components of signals or changes in theiramplitudes. When the phase deviation ΔT_(B) between the signals shown inequations (56) and (57) is detected by using the lock-in amplifier 105,the amount of relative deviation between the diffraction gratings 74 and48 along the x orientation can be determined on the basis of theequation: ##EQU9##

In similar manner, when the phase deviation ΔT_(C) between the signalsshown in equations (58) and (59) is detected by using the lock-inamplifier 104, the amount of relative deviation between the diffractiongratings 74 and 49 along the x orientation can be determined on thebasis of the equation: ##EQU10## In addition, the relative deviationbetween the diffraction gratings 48 and 49 can be determined bymeasuring the difference between the deviation between the diffractiongratings 74 and 48, and the deviation between the diffraction gratings74 and 49. The above is performed by a computing unit 111 when theoutputs from the lock-in amplifiers 104 and 105 are received. In thisembodiment, also, a phase deviation for the same deviation is two timesgreater than that using beat signals whose phases are fixed as areference. If the pitches of the diffraction gratings 74, 48 and 49 areset at 2 μm, the wavelength of light emitted from the light source 70 isset at λ=0.6328 μm; and the diffraction angle of ±first-order diffractedlight when light is incident perpendicularly to the diffraction grating74 is denoted as θ.sub.±1, θ.sub.±1 =sin⁻¹ (0.6328/2)=18.4° on the basisof the relation:

    θ.sub.±m =sin (mλ/P) (m: order of diffraction) (60)

Therefore, to cause light incident on the diffraction gratings 48 and 49to be diffracted upward perpendicularly to the wafer 23, the mirrors 91and 92 should be set so that the right and left incident angles areequal to θ.sub.±1.

In this measurement, a phase difference can be detected at λ/500. Thepositional deviation between the diffraction gratings 74 and 48, or thepositional deviation between the diffraction gratings 74 and 49corresponds to 0.0021 μm.

FIG. 9 shows a specific example of the frequency shifter 71. Referencenumerals 121 and 126 denote polarization beam splitters; referencenumerals 122 and 123 denote acoustic optical modulators; and referencenumerals 124 and 125 denote mirrors. If acoustic optical modulators of80 and 123 MHz are used as modulators 122 and 123, respectively, afrequency difference of 1 MHz in which polarized states intersect atright angles with each other is obtained between two light beams.

If the deviation of a first brazed grating pattern from a second brazedgrating pattern on the basis of the above-described principles in theabove manner is determined, the alignment accuracy of a semiconductorexposure apparatus, and an amount of deviation between real elementpatterns formed by the first and second brazing can be detected.

FIG. 10 is a view illustrating the fifth embodiment of the presentinvention. Light beams emitted from the light source 70 are made intolight beams u₁ (P polarization, frequency f₁) and u₂ (S polarization,frequency f₂) whose frequencies f are slightly different from each otherby means of the frequency shifter 71, the polarization planes thereofintersecting at right angles with each other. Complex amplitude displaysof the light beams u₁ and u₂ can be expressed as in the followingequations below if φ₁ and φ₂ denote initial phases, C₁₀ and C₂₀ denoteamplitudes, w₁ and w₂ denote angular frequencies, and w₁ =2π f₁ and w₂=2πf₂ :

    u.sub.1 =C.sub.10 ·exp {i (w.sub.1 t+φ.sub.1)}(61)

    u.sub.2 =C.sub.20 ·exp {i (w.sub.2 t+φ.sub.2)}(62)

The diameters of the two light beams u₁ and u₂ on a common optical pathare condensed by the beam expander 72. The direction of travel thereofis changed by the mirror 73 and made to perpendicularly enter the lineardiffraction grating 48 and 49 on the wafer 50.

In FIG. 10, when the deviation of the diffraction gratings 48 and 49from a reference position are denoted as x_(B) and x_(C), respectively,phases 2πx_(B) /P and 2πx_(C) /P with P as the pitch of the grating areadded to the +first-order diffracted light beams u_(1B) (1) and u_(2B)(1) (diffracted light beams of u₁ and u₂, respectively) from thediffraction grating 48, and +first-order diffracted light beams u_(1C)(1) and u_(2C) (1) (diffracted light beams of u₁ and u₂, respectively)from the diffraction grating 49, indicated by an optical path R1. Thecomplex amplitudes thereof are expressed as follows:

    u.sub.1B (1)=C.sub.1B exp {i (w.sub.1 t+φ.sub.1 +φ.sub.B)}(63)-1

    u.sub.2B (1)=C.sub.2B exp {i (w.sub.2 t+φ.sub.2 +φ.sub.B)}(63)-2

    u.sub.1C (1)=C.sub.1C exp {i (w.sub.1 t+φ.sub.1 +φ.sub.C)}(63)-3

    u.sub.2C (1)=C.sub.2C exp {i (w.sub.2 t+φ.sub.2 +φ.sub.C)}(63)-4

where u_(1B), u_(2B), u_(1C), and u_(2C) are amplitudes, φ_(B) =2πX_(B)/P and φ_(C) =2πX_(C) /P. In FIG. 10, complex amplitudes of -first-orderdiffracted light beams u_(1B) (-1) and u_(2B) (-1) (diffracted lightbeams of u₁ and u₂, respectively) from the diffraction grating 48, and-first-order diffracted light beams u_(1C) (-1) and u_(2C) (-1)(diffracted light beams of u₁ and u₂, respectively) from the diffractiongrating 49, indicated by an optical path R₂, are expressed as follows:

    u.sub.1B (-1)=C.sub.1B exp {i (w.sub.1 t+φ.sub.1 -φ.sub.B)}(64)-1

    u.sub.2B (-1)=C.sub.2B exp {i (w.sub.2 t+φ.sub.2 -φ.sub.B)}(64)-2

    u.sub.1C (-1)=C.sub.1C exp {i (w.sub.1 t+φ.sub.1 -φ.sub.C)}(64)-3

    u.sub.2C (-1)=C.sub.2C exp {i (w.sub.2 t+φ.sub.2 -φ.sub.C)}(64)-4

±First-order diffracted light beams are deflected by mirrors 91 and 92respectively and made to enter a polarization beam splitter 134. Lightbeams u_(1B) (1), u_(1C) (1), u_(1B) (-1), and u_(1C) (-1) of Ppolarization are transmitted through the polarization beam splitter 134.Light beams u_(2B) (1), u_(2C) (1), u_(2B) (-1), and u_(2C) (-1) of Spolarization are reflected by the polarization beam splitter 134.Thereafter, the polarization planes thereof are aligned by Glan-Thompsonprisms 135 and 136 and made to interfere with each other. Of the lightbeams emerging from the Glan-Thompson prism 135, the intensity changeV_(BL) of the interference light beams of light diffracted by thediffraction grating 48 and the intensity change V_(CL) of theinterference light beams of light diffracted by the diffraction grating49 are respectively as follows:

    V.sub.BL =|u.sub.1B (-1)+u.sub.2B (1)|.sup.2 =C.sup.2.sub.1B +C.sup.2 .sub.2B +2C.sub.1B C.sub.2B cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)+2φ.sub.B }     (65)

    V.sub.CL =|u.sub.1C (-1)+u.sub.2C (1)|.sup.2 =C.sup.2.sub.1C +C.sup.2 .sub.2C +2C.sub.1C C.sub.2C cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)+2φ.sub.C }     (66)

Of the light beams emerging from the Glan-Thompson prism 136, theintensity change V_(BR) of the interference light beam of lightdiffracted by the diffraction grating 48, and the intensity changeV_(CR) of the interference light beam of the light diffracted by thediffraction grating 49, are:

    V.sub.BR =|u.sub.1B (1)+u.sub.2B (-1)|.sup.2 =C.sup.2.sub.1B +C.sup.2 .sub.2B +2C.sub.1B C.sub.2B cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)+2φ.sub.B }     (67)

    V.sub.CR =|u.sub.1C (1)+u.sub.2C (-1)|.sup.2 =C.sup.2.sub.1C +C.sup.2 .sub.2C +2C.sub.1C C.sub.2C cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)+2φ.sub.C }     (68)

Furthermore, the light beams are spatially separated by mirrors 137 and138 into interference light beams 145 (shown by equation (65)) and 147(shown by equation (66)) of diffracted light from the diffractiongrating 48, and interference light beams 146 (shown by equation (66))and 148 (shown by equation (68)) of diffracted light from thediffraction grating 49. The intensity changes of the respectiveinterference light beams are detected by photoelectric converters 140,143, 141 and 142. The electrical signals are sent to the lock-inamplifiers 105 and 104. At this time, as the initial phase of light canbe erased, phase deviations ΔT_(B) and ΔT_(C) detected by the lock-inamplifiers 105 and 104 are expressed as follows:

    ΔT.sub.B =4φ.sub.B =8πx.sub.B /P, ΔT.sub.C =4φ.sub.C =8πx.sub.C /P.

The deviation is measured by the computing unit 111 on the basis of theabove equations as described in the fourth embodiment.

FIG. 11 is a view illustrating the sixth and seventh embodiments of thepresent invention. In the sixth embodiment, high-order diffracted light(±m-th order: m=2, 3, 4 . . . ) is used, whereas a case in which adeviation is detected by using ±first-order diffracted light from thediffraction gratings 74, 48 and 49 is used, has been shown in the fourthand fifth embodiments.

In FIG. 11, if the pitches of the diffraction gratings 74, 48 and 49 areset at P=2 μm, the wavelength of the light from light source 70 (notshown) is set at λ=0.6328 μm, since the diffraction angles θ₁ and θ₂ of+second-order diffracted light and -second-order diffracted light whenthe light enters the diffraction grating 74 perpendicularly. Then, θ₁=θ₂ =sin (2×0.6328/2)=39.3° on the basis of equation (60). To causelight which has entered the diffraction gratings 48 and 49 to bediffracted upward perpendicular from the wafer 50, the mirrors 91 and 92should be set so that incident angles θ₃ and θ₄ of the light beams 76',77', 78 and 79 with respect to the diffraction gratings 48 and 49 areequal to θ₁ (θ₂). In similar manner, the incident angle should be setfor ±third-order diffracted light in such a way that θ±3=sin(3×0.6328/2)=71.7°.

When ±m-th-order diffracted light is used, phase terms φ_(Am), φ_(Bm)and φ_(Cm) corresponding to φ_(A), φ_(B) and φ_(C) in equations (56) to(59) are expressed as follows:

    φ.sub.Am =2mπx.sub.A /P                             (69)

    φ.sub.Bm =2mπx.sub.B /P                             (70)

    φ.sub.Cm =2mπx.sub.C /P                             (71)

where x_(A), x_(B), and x_(C) denote a deviation of diffraction gratings74, 48 and 49, respectively, along the x orientation from the samereference.

Therefore, if the deviations of the diffraction gratings 48 and 49relative to the diffraction grating 74 are expressed in terms of a phaseamount, it follows that: ##EQU11##

Therefore, if high-order diffracted light is used for measurements, aphase amount indicating the deviation of a diffraction grating along thex orientation can be determined with a higher degree of sensitivity. Forexample, if ±m-th-order diffracted light is used for measurements,sensitivity is increased m times more than when ±first-order diffractedlight is used.

In FIG. 11, in the fourth and sixth embodiments, light beams 76' and 77'are irradiated from the left, and light beams 78 and 79 are irradiatedfrom the right, onto the entire surface of the diffraction gratings 48and 49 at the same incident angle (θ₃ =θ₄). Diffracted light beams whoseabsolute values or order are the same (e.g., +m-th order and -m-thorder, m=1, 2, 3 . . . ) are made to interfere with each other and areused for measurements. In the seventh embodiment, the incident angles oflight beams 76' and 77', and light beams 78 and 79 with respect to thediffraction gratings 48 and 49, are adjusted by varying the angles ofthe mirrors 91 and 92. Diffracted light beams whose absolute values areof different orders (e.g., +m-th order and -n-th order, m=1, 2, 3 . . ., n=1, 2, 3 . . . , |m|≠|n|) may be made to interfere with each otherand the deviation is detected.

In FIG. 11, the mirrors 91 and 92 are adjusted so that +m-th orderdiffracted light beams of the light beams 76' and 77' with respect tothe diffraction gratings 48 and 49 and -n-th order diffracted lightbeams of the light beams 78 and 79 with respect to diffraction gratings48 and 49 are diffracted upward perpendicular from the wafer 50, andincident angles θ₃ and θ₄ with respect to the diffraction gratings 48and 49 are determined. At this time, if ±1-th order light beams are usedfor the diffracted light of the diffraction grating 74, the followingrelation is satisfied with the phase term corresponding to φ_(A) inequations (48) to (55) as φ_(A1) :

    φ.sub.A1 =2 1π x.sub.A /P                           (74)

If φ_(B) in equations (48) and (49) is denoted by φ_(Bm), and if φ_(B)in equations (50) and (51) is denoted by φ_(Bn), the following relationsare satisfied:

    φ.sub.Bm =2mπ x.sub.B /P                            (75)

    φ.sub.Bn =2nπ x.sub.B /P                            (76)

Furthermore, if φ_(C) in equations (48) and (49) is denoted by φ_(Cm),and if φ_(C) in equations (50) and (51) is denoted by φ_(Cn), thefollowing relations are satisfied:

    φ.sub.Cm =2mπ x.sub.C /P                            (77)

    φ.sub.Cn =2nπ x.sub.C /P                            (78)

At this time, intensity changes V'_(BP), V'_(BS), V'_(CP) and V'_(CS) ofinterference light beams 107, 108, 109 and 110 in FIG. 8 are expressedas follows:

    V'.sub.BP =C.sup.2.sub.1 +C.sup.2.sub.2 +2C.sub.1 C.sub.2 cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 φ.sub.1)+(φ.sub.Bm +φ.sub.Bn)+2φ.sub.A1 }                            (79)

    V'.sub.BS =C.sup.2.sub.1 +C.sup.2.sub.2 +2C.sub.1 C.sub.2 cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 φ.sub.1)-(φ.sub.Bm +φ.sub.Bn)-2φ.sub.A1 }                            (80)

    V'.sub.CP =C.sup.2.sub.1 +C.sup.2.sub.2 +2C.sub.1 C.sub.2 cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)+(φ.sub.Cm +φ.sub.Cn)+2φ.sub.A1 }                            (81)

    V'.sub.CS =C.sup.2.sub.1 +C.sup.2.sub.2 +2C.sub.1 C.sub.2 cos {(w.sub.2 -w.sub.1) t+(φ.sub.2 -φ.sub.1)-(φ.sub.Cm +φ.sub.Cn)-2φ.sub.A1 }                            (82)

Therefore, if the deviation of the diffraction gratings 48 and 49 withrespect to the diffraction grating 74 is represented in terms of a phaseamount, it follows that: ##EQU12## The subtraction of the right side ofequation (83) from the right side of equation (84) yields the following:##EQU13## Therefore, a relative deviation between the diffractiongratings 48 and 49 along the x orientation can be determined by equation(85) on the basis of the difference between the phase amounts detectedby the lock-in amplifiers 104 and 105.

FIG. 12 shows the eighth embodiment of the present invention. In thethird embodiment, to separate interference light beams 61, 62, 63 and64, as shown in FIG. 7, a light beam is made to enter the polarizationbeam splitter 52 first. After the light beam is divided in two: (a) Ppolarized light beams 61 and 63, and (b) S polarized light beams 62 and64, the light beams are separated by means of the edge mirror 53 (54)into interference light beam 61 (62) by light diffracted by thediffraction grating 48 and interference light beam 63 (64) by lightdiffracted by the diffraction grating 49. In this embodiment, as shownin FIG. 12, after the light beams are divided in two by means of amirror 150: (a) interference light beams 61 and 62 formed by light beamsdiffracted by the diffraction grating 48, and (b) interference lightbeams 63 and 64 formed by light beams diffracted by the diffractiongrating 49. The light beams are separated into P polarized light beams61 (63) and S polarized light beams 62 (64) by means of a polarizationbeam splitter 151 (152).

FIGS. 13 and 14 are views illustrating the ninth and tenth embodimentsof the present invention, respectively. There is no offset of a patterncentral position, in a direction in which a positional offset isdetected, between the diffraction gratings 48 and 49 used for themeasurements in the third to eighth embodiments. However, in thisembodiment, the diffraction gratings 48 and 49 are previously arrangedto be offset by a known amount x of the diffraction gratings 48 and 49,and the offset is subtracted to detect the deviation Δx of the pattern.FIG. 13 shows a condition in which an offset is set in a directionintersecting at right angles with the direction in which a positionaloffset is detected. FIG. 14 shows a condition in which an offset is setin only a direction in which a positional offset is detected.

As described above, according to the above-described embodiments,sensitivity can be obtained which is approximately two times greaterthan with a measuring method using a heterodyne interference method withbeat signals whose phases are fixed as a reference.

A measuring apparatus of the embodiments which will now be describedincludes a light-beam forming unit for forming a first pair of beamshaving different frequencies and a second pair of beams having differentfrequencies which are combined in such a manner as to generate beatsignals having the same frequency; an irradiation unit for irradiatingeach of the pairs of beams in such a way that a light beam of one of thepair of beams having a low frequency and a light beam of the other pairof beams having a high frequency of the first and second light beams arediffracted at a first order by means of diffraction unit and that alight beam of one of the pair of beams having a high frequency and alight beam of the other pair of beams having a low frequency arediffracted at a second order whose sign is different from that of thefirst order by means of the diffraction unit; and displacementinformation detection unit for obtaining relative displacementinformation of the diffraction unit by comparing a first beat signalobtained by causing the first pair of diffracted beams to interfere witheach other with a second beat signal obtained by causing the second pairof diffracted beams to interfere with each other.

Before the embodiments are explained, the technology which is aprerequisite for subsequent embodiments will be described below withreference to FIG. 15. FIG. 15 is a schematic view of a length measuringapparatus using the prerequisite technology.

In FIG. 15, first a monochromatic light beam from a semiconductor laserLD is divided into two light beams L1 and L2 by a polarization beamsplitter BS1. The light beams L1 and L2 are made to enter acousticoptical modulators AO1 and AO2, respectively. Frequencies f₁ and f₂ ofoutgoing light beams whose polarization planes are tilted by 90°relative to each other are shifted so that the frequencies differ to anextent that the beat signals thereof can be electrically observed. Thelight beams are merged by a half mirror HM.

A part of this merged light beam is extracted by a beam splitter BS2,and an optical heterodyne signal is obtained as a reference signal by aphotoreceptor element PD1. A polarization plate PP1 whose polarizationorientation is tilted by 45° is inserted at a location before the PD1 tocause the polarization planes of the two light beams to be aligned andto cause the light beams to interfere with each other at that time.

When the remaining light beam divided by BS2 enters the diffractiongrating GS perpendicularly and is diffracted, the phase δ of thediffraction grating GS is added to the diffraction wave front. If it isassumed that the initial phase of an incident beam is 0, the phase beamof the diffracted waves is exp {i (wt+mδ)}, where m is the order ofdiffraction. For example, the +first-order light beam and -first-orderlight beam are exp {i (wt+mδ)} and exp {i (wt-mδ)}, respectively. Toextract light beams only of frequency f₁ for +first-order light beam L3and light beams only of frequency f₂ for -first-order light beam L4,polarization filters PF1 and PF2 are disposed inside the optical pathsfor the light beams L3 and L4, respectively. The light beams L3 and L4enter corner cube prisms CC1 and CC2, are reflected in a directionparallel and opposite to the incidence direction, respectively, are madeto return to a point P2 on the diffraction grating GS, are diffracted asecond time at the same order as that of the first diffraction to becomeone light beam, interfere with each other and enter the photoreceptorelement PD2.

There is a phase lead of one wavelength in the phase of the +first-orderlight beam L3 for a displacement corresponding to one pitch of thediffraction grating GS along the x orientation. There is a phase delayof one wavelength in the phase of the -first-order light beam L4. Asthese light beams are once more reflected by the corner cube prisms CC1and CC2 and diffracted at the same order as before, a phase differencefor four wavelengths is added to the phases of the two light beams whenthe light beams are merged.

If a light beam having a frequency f₁ is represented by u₁ =a exp {i (w₁t)}, and a light beam having a frequency f₂ is represented by u₂ =b exp{i (w₂ t)} (where a, b are constants, t is time, and i is an imaginaryunit), an optical heterodyne signal obtained by the photoreceptorelement PD1 as a reference signal is expressed as follows:

    I.sub.REF =a.sup.2 +b.sup.2 +2ab cos (w.sub.1 -w.sub.2) t

Since, in the above equation, w₁ =2π f₁ and w₂ =2π f₂, this signal is asignal with a frequency corresponding to the difference between f₁ andf₂. Since the phase δ of the diffraction grating GS is added to the+first-order light beam L3 each time the light beam L3 is diffracted andfinally the +first-order light beam is diffracted two times, thefollowing expression can be made:

    u'.sub.1 =a' exp {i (w.sub.1 t+2δ)}

where a' is a constant.

Since the phase δ of the diffraction grating GS is subtracted from the-first-order light beam L4 each time the light beam L4 is diffracted andfinally the -first-order light beam is diffracted two times, a lightbeam expressed as

    u'.sub.2 =b' exp {i (w.sub.2 t+2δ)}

(where b' is a constant) is incident on the photoreceptor element PD2.Therefore, an optical heterodyne signal obtained by the photoreceptorelement PD2 is expressed as follows:

    I.sub.SIG =a'.sup.2 +b'.sup.2 +2a'b' cos {(w.sub.1 -w.sub.2) t+4δ}

The frequency of this signal is the same as that of the referencesignal, but the phase of the optical heterodyne signal is out of phasewith the reference signal by an amount 4δ proportional to the amount ofmovement of the diffraction grating GS.

Two optical heterodyne signals obtained by the photoreceptor elementsPD1 and PD2 are input to a phase difference detector PDC. The phasedifference between the signals is detected to measure the amount ofmovement of the diffraction grating GS. If the grating constant of thediffraction grating GS is set at 1.6 μm and the amount of movement ofdiffraction grating GS is denoted as x, the following relation issatisfied: ##EQU14## Therefore, when a phase deviation of one cycle,i.e., 2π [rad], is detected, it is clear that the diffraction grating GSis moved by 1.6 μm≈4=0.4 μm. Detection of an amount of movement with ahigh degree of resolution is made possible by making the minimumdetection phase difference sufficiently smaller than one cycle. If aphase difference detector which is capable of resolving up to, forexample, 0.2°, is used, theoretically, a displacement up to 0.22 [nm]can be measured.

Embodiments will be explained below with reference to the accompanyingdrawings on the basis of the prerequisite technology described above..

FIG. 16 is a schematic view of a length measuring apparatus of theeleventh embodiment of the present invention. Components in FIG. 16which are the same as those shown in FIG. 15 are given the samereference numerals.

In FIG. 16, first a monochromatic light beam from a semiconductor laserLD is divided into two light beams L1 and L2 by the polarization beamsplitter BS1. The light beams L1 and L2 are made to enter the acousticoptical modulators AO1 and AO2, respectively. Frequencies f₁ and f₂ ofoutgoing light beams whose polarization planes are tilted by 90°relative to each other are shifted so that the frequencies differ to anextent that the beat signals thereof can be electrically observed. Thelight beams are merged by the half mirror HM.

The merged light beam is divided into two beams by a beam splitter BS3.The transmitted light beam is reflected by a mirror MR3. The beams enterperpendicularly to the diffraction grating GS at points P5 and P3,respectively, and are diffracted. To extract light beams only offrequency fl for +first-order light beam L7 diffracted at point P5, andlight beams only of frequency f₂ for -first-order light beam L8,polarization filters PF5 and PF6 are disposed inside the optical pathsfor the light beams L7 and L8, respectively. Similarly, to extract lightbeams only of frequency f₂ for +first-order light beam L5 diffracted atpoint P3 and light beams only of frequency f₁ for -first-order lightbeam L6, polarization filters PF3 and PF4 are disposed inside theoptical paths for the light beams L5 and L6, respectively. The lightbeams L7, L8, L5 and L4 enter corner cube prisms CC5, CC6, CC3 and CC4,respectively, are reflected in a direction parallel and opposite to theincidence direction, are made to return to points P6 and P4 on thediffraction grating GS, are diffracted a second time at the same orderas that of the first diffraction to become one light beam, interferewith each other and enter the photoreceptor element PD2. The light beamsare diffracted a second time at the same order as that of the firstdiffraction at points P6 and P4. Two light beams are merged at each ofthese two points to become one light beam. The merged light beam from P6being made to enter the photoreceptor element PD3, and the merged lightbeam from P4 being made to enter the photoreceptor element PD4.Polarization plates PP3 and PP4 whose polarization orientations aretilted by 45° to cause the light beams to interfere with each other withtheir polarization planes aligned are disposed at a location before thephotoreceptor element PD3 and PD4, respectively.

There is a phase lead of one wavelength in the phases of the+first-order light beams L7 and L5 for a displacement corresponding toone pitch of the diffraction grating GS along the x orientation. Thereis a phase delay of one wavelength in the phase of the -first-orderlight beams L8 and L6. As these light beams are once more reflected bycorner cube prisms and diffracted at the same order as before, a phasedifference for four wavelengths is added to the phase of the mergedlight beams L7 and L8 when the light beams are merged again at point P6.Also, a phase difference for four wavelengths is added to the lightbeams L5 and L6 merged at P4.

If it is assumed that w₁ =2π f₁ and w₂ =2π f₂, as described above, thelight beam L1 is expressed as u₁ =a·exp {i (w₁ t)}, and the light beamL2 is expressed as u₂ =a· exp {i (w₂ t)}. The phase δ corresponding tothe amount of movement x of diffraction grating GS is expressed asfollows with the grating constant of the diffraction grating GS as p:##EQU15## Since the phase δ of the diffraction grating GS is added tothe +first-order light beam L7 each time it is diffracted and+first-order diffracted a total of two times, the light beam can beexpressed by the following equation when it is incident on thephotoreceptor element PD3:

    u".sub.1 =a" exp {i (w.sub.1 t+2δ)}

where a" is a constant. Since the phase δ of the diffraction grating GSis subtracted from the -first-order light beam L8 each time it isdiffracted and finally the -first-order beam is diffracted two times, alight beam expressed as

    u'.sub.2 =b' exp {i (w.sub.2 t+2δ)}

(where b' is a constant) is incident on the photoreceptor element PD3.Therefore, an optical heterodyne signal obtained by the photoreceptorelement PD3 is expressed as follows:

    I.sub.PD3 =a".sup.2 +b"2+2a"b" cos {(w.sub.1 -w.sub.2) t+4δ}

The frequency of this signal is the same as the difference between f₁and f₂. The phase thereof is added because of diffraction by an amount4δ proportional to the amount of movement of the diffraction grating GS.Since the phase δ of the diffraction grating GS is added to the+first-order light beam L5 each time it is diffracted and the+first-order beam is diffracted a total of two times, the followingequation can be made when the light beam is incident on thephotoreceptor element PD4:

    u'".sub.2 =b'" exp {i (w.sub.2 t+2δ)}

where b'" is a constant. Since the phase δ of the diffraction grating GSis subtracted from the -first-order light beam L6 each time it isdiffracted and finally -first-order beam is diffracted two times, alight beam expressed as

    u'".sub.1 =a'" exp {i (w.sub.1 t+2δ)}

(where a'" is a constant) is incident on the photoreceptor element PD4.Therefore, an optical heterodyne signal obtained by the photoreceptorelement PD4 is expressed as follows:

    I.sub.PD4 =a'".sup.2 +b'".sup.2 +2a'"b'" cos {(w.sub.1 -w.sub.2) t-4δ}

The frequency of this signal is the same as that obtained by thephotoreceptor element PD3, and an amount 4δ proportional to the amountof movement of the diffraction grating GS is subtracted by diffractionfrom the phase. Two optical heterodyne signals obtained by thephotoreceptor elements PD3 and PD4 are input to the phase differencedetector PDC. The phase difference between the signals is detected bythe detector PDC to measure the amount of movement of the diffractiongrating GS. If the grating constant of the diffraction grating GS is setat 1.6 μm and the amount of movement of diffraction grating GS isdenoted as x, the following relation is satisfied: ##EQU16## Therefore,when a phase deviation of one cycle, i.e., 8δ=2π [rad], is detected, itis clear that the diffraction grating GS is moved by 1.6 μm≈8=0.2 μm.This means that the amount of a displacement which can be detected by aphase difference of one cycle is one half that for the above-mentionedapparatus of FIG. 15. Accordingly, even if a phase difference detectorhaving the same resolution is used, a minimum detection displacementamount of the apparatus of this embodiment is one half that of theapparatus of FIG. 15, and a higher resolution is obtained. The use ofthe above-mentioned phase difference detector capable of resolving up to0.2° permits a displacement up to 0.11 [nm] to be measuredtheoretically.

FIG. 17 shows the twelfth embodiment of the present invention. Althoughin this embodiment, the optical system around diffraction gratingsextracts in the same form as in the eleventh embodiment, a referencesignal is extracted and the method of detecting a phase difference ismodified. Components which are the same as those described above aregiven the same reference numerals below.

In FIG. 17, first a monochromatic light beam from the semiconductorlaser LD is divided into two light beams L1 and L2 by a polarizationbeam splitter BS1. The light beams L1 and L2 are made to enter acousticoptical modulators AO1 and AO2, respectively. Frequencies f₁ and f₂ ofoutgoing light beams whose polarization planes are tilted by 90°relative to each other are shifted so that the frequencies differ to anextent that the beat signals thereof can be electrically observed. Thelight beams are merged by the half mirror HM.

A part of this merged light beam is extracted by the beam splitter BS2,and an optical heterodyne signal is obtained as a reference signal bythe photoreceptor element PD1. To cause the polarization planes of thetwo light beams to be aligned and to cause the light beams to be made tointerfere with each other at that time, the polarization plate PP1 whosepolarization orientation is tilted by 45° is inserted at a locationbefore the PD1.

The remaining light beam divided by BS2 is further divided into two bythe beam splitter BS3. The transmitted light beams from beam splitterBS3 are reflected by the mirror MR3, and the transmitted and reflectedlight beams enter the diffraction grating GS perpendicularly at pointsP5 and P3, respectively, and are diffracted. To extract light beams onlyof frequency fl for +first-order light beam L7 diffracted at point P5and light beams only of frequency f₂ for -first-order light beam L8,polarization filters PF5 and PF6 are disposed inside the optical pathsfor the light beams L7 and L8, respectively. Similarly, to extract lightbeams only of frequency f₂ for +first-order light beam L5 diffracted atpoint P3 and light beams only of frequency f₁ for -first-order lightbeam L6, polarization filters PF3 and PF4 are disposed inside theoptical paths for the light beams L5 and L6, respectively. The lightbeams L7, L8, L5 and L6 enter corner cube prisms CC5, CC6, CC3 and CC4,respectively, are each reflected in a direction parallel and opposite tothe incidence direction, respectively, and are made to return to pointsP6 and P4 on the diffraction grating GS. The light beams are diffractedat these two points a second time at the same order as that of the firstdiffraction to become one light beam. The merged light beams from pointP6 enter the photoreceptor element PD3, and the merged light beams frompoint P4 enter the photoreceptor element PD4. To cause the polarizationplanes of the two merged light beams to be aligned and to cause thelight beams to interfere with each other, polarization plates PP3 andPP4 whose polarization orientations are tilted by 45° are inserted atlocations before the photoreceptor elements PD3 and PD4, respectively.

There is a phase lead of one wavelength in the phase of the +first-orderlight beams L7 and L5 for a displacement corresponding to one pitch ofthe diffraction grating GS along the x orientation. There is a phasedelay of one wavelength in the phase of the -first-order light beam L8and L6. As each of these light beams is reflected by the corner cubeprisms and diffracted once more at the same order as before, a phasedifference for four wavelengths is added to the phase of the mergedlight beams L7 and L8 when the light beams are merged at point P6. Also,a phase difference for four wavelengths is added to the phase of themerged light beams L5 and L6 when the light beams are merged at pointP4.

As described above, if a light beam having a frequency f₁ is representedby u₁ =a·exp {i (w₁ t)}, and if a light beam having a frequency f₂ isrepresented by u₂ =b exp {i (w₂ t)}, an optical heterodyne signalobtained by the photoreceptor element PD1 as a reference signal isexpressed as follows:

    I.sub.REF =a.sup.2 +b.sup.2 +2ab cos (w.sub.1 -w.sub.2) t.

Since, in the above equation, w₁ =2π f₁ and w₂ =2π f₂, this signal is asignal having a frequency corresponding to the difference between f₁ andf₂. The phase δ of the diffraction grating GS corresponding to theamount x of movement of the diffraction grating GS is expressed asfollows, as was previously mentioned: ##EQU17## Since the phase δ of thediffraction grating GS is added to the +first-order light beam L7 eachtime it is diffracted and the finally +first-order diffracted beam isdiffracted two times, the following expression can be made when thelight beam is incident on the photoreceptor element PD3:

    u".sub.1 =a" exp {i (w.sub.1 t+2δ)}.

Since the phase δ of the diffraction grating GS is subtracted from the-first-order light beam L8 each time it is diffracted and the finally-first-order diffracted beam is diffracted two times, a light beamexpressed as

    u".sub.2 =b" exp {i (w.sub.2 t-2δ)}

is incident on the photoreceptor element PD3. Therefore, an opticalheterodyne signal obtained by the photoreceptor element PD3 is expressedas follows:

    I.sub.PD3 =a".sup.2 +b".sup.2 +2a"b" cos {(w.sub.1 -w.sub.2) t+4δ}.

The frequency of this signal is the same as that of the referencesignal. The phase thereof leads that of the reference signal, by anamount 4δ proportional to the amount of movement of the diffractiongrating GS. Since the phase δof the diffraction grating GS is added tothe +first-order light beam L5 each time it is diffracted and thefinally +first-order diffracted beam is diffracted two times, thefollowing expression can be made when the light beam is incident on thephotoreceptor element PD4:

    u'".sub.2 =b'" exp {i (w.sub.2 t+2δ)}

Since the phase δ of the diffraction grating GS is subtracted from the-first-order light beam L6 each time it is diffracted and the finally-first-order diffracted beam is diffracted two times, a light beamexpressed as

    u'".sub.1 =a'" exp {i (w.sub.1 t-2δ)}

is incident on the photoreceptor element PD4. Therefore, an opticalheterodyne signal obtained by the photoreceptor element PD4 is expressedas follows:

    I.sub.PD4 =a'".sup.2 +b'".sup.2 +2a'"b'" cos {(w.sub.1 -w.sub.2) t-4δ}

The frequency of this signal is the same as that of the referencesignal, and the phase thereof is delayed with respect to that of thereference signal by an amount 4δ proportional to the amount of movementof the diffraction grating GS. Two optical heterodyne signals obtainedby the photoreceptor elements PD3 and PD4 are input to the phasedifference detector PDCA. The phase difference between the signals isdetected by the detector PDCA to measure the amount of movement of thediffraction grating GS. If the grating constant of the diffractiongrating GS is set at 1.6 μm and the amount of movement of diffractiongrating GS is denoted as x, the following relation is satisfied:##EQU18## Therefore, when a phase deviation of 8δ=2π [rad] is detected,it is clear that the diffraction grating GS is moved by 1.6 μm≈8=0.2 μm.This is the same as in the first embodiment. The use of theabove-mentioned phase difference detector capable of resolving up to0.2° permits a displacement up to 0.11 [nm] to be measuredtheoretically. In this embodiment, the output from the detector PDCA isinput to a central processing unit (CPU) C, whereby the signals areprocessed and an amount of displacement is computed.

Photoreceptor elements PD1 and PD3 detect a phase difference in a phasedifference detector PDCB in the same manner as above and compare a phasedifference obtained by a phase difference detector PDCC from thephotoreceptor elements PD1 and PD4. At that time, when there is atemperature difference between two optical paths because of, forexample, air disturbance, though the absolute values of the two phasedifferences are equal, being 4δ, these two phase differences are notequal. Therefore, when a difference between these phase differences isdetected by the CPU, it is detected that the measured value iserroneous. When a difference between these phase differences exceeds anallowable value, erroneous inputting of a measured value can beprevented by the CPU performing the following: (1) sending a commandsignal to an unillustrated actuator in order to stop a fine movement ofthe diffraction grating, that is, the measurement is temporarilystopped, or (2) erasing a signal from the phase difference detector PDCAat that time.

FIG. 18 shows the thirteenth embodiment of the present invention, inwhich the construction of the apparatus shown in FIG. 18 is simplifiedby providing one optical path, whereas previous embodiments have twosimilar optical paths.

In FIG. 18, first a monochromatic light beam from the semiconductorlaser LD is divided into two light beams L1 and L2 by the polarizationbeam splitter BS1. The light beams L1 and L2 are made to enter acousticoptical modulators AO1 and AO2, respectively. Frequencies f₁ and f₂ ofthe outgoing light beams whose polarization planes are tilted by 90°relative to each other are shifted so that the frequencies differ to anextent that the beat signals thereof can be electrically observed. Thelight beams are merged by the half mirror HM1.

This merged light beam is divided into two by a half mirror HM2. Onelight beam is made to enter the diffraction grating GS at point P1. The+first-order diffracted light beam path through an optical system formedby two polarization plates 1P and 2P shown in FIG. 19, whosepolarization directions intersect at right angles with respect to eachother, and a λ/2 plate 3P. Only the S-polarized diffracted light beamshaving frequency f₁ are converted into P-polarized light beams, are madeto enter the corner cube prism CC1, are reflected and are made to enterpoint P2 on the diffraction grating GS. In contrast, -first-orderdiffracted light beams are made to enter an optical system such as theoptical system shown in FIG. 19 tilted axially by 90° (i.e., the opticalsystem formed of polarization plates 1P' and 2P', and a λ/2 plate 3P').Only the P-polarized diffracted light beams having frequency f₂ areconverted into S-polarized light beams, made to enter the corner cubeprism CC2, reflected and made to enter point P2 on the diffractiongrating GS. The two light beams which have entered the point P2 arediffracted a second time at the same order as at the first time, aremerged and transmitted through the half mirror HM3 as one light beam,and enter the photoelectric conversion element PD2. To cause thepolarization planes of the two light beams to be aligned and to causethe light beams to interfere with each other, a polarization plate PP2whose polarization orientation is tilted by 45° is inserted at alocation before the PD2. There is a phase lead of one wavelength in thephase of the +first-order light beam for a displacement corresponding toone pitch of the diffraction grating GS along the x orientation. Thereis a phase lag of one wavelength in the phase of the -first-order lightbeam. As these light beams are reflected by the corner cube prisms anddiffracted once more at the same order as before, a phase difference forfour wavelengths are added to the light beams having a frequencies f₁and f₂ when the light beams are merged at point P2.

The remaining light beams which have been transmitted through the halfmirror HM2 are reflected by the half mirror HM3, and made to enter thediffraction grating GS at point P2. The +first-order diffracted lightbeams are made to enter the corner cube prism CC1, then pass through theoptical system such that the optical system shown in FIG. 19 is tiltedaxially by 90° in a direction opposite to the previous case. TheP-polarized diffracted light beams only having a frequency f₂ areconverted into S-polarized light beams and made to enter the diffractiongrating GS at point P2. In contrast, the -first-order diffracted lightbeams are made to enter the optical system shown in FIG. 19 in adirection opposite to the previous case. The S-polarized diffractedlight beams only having a frequency f₁ are converted into P-polarizedlight beams and made to enter the diffraction grating GS at point Pl.The two light beams which have entered point Pl are diffracted again andmerged. The light beams are transmitted through the half mirror HM2 asone light beam and made to enter the photoelectric conversion elementPD1. To cause the polarization planes of the light beams to be alignedand to cause the light beams to interfere with each other, apolarization plate PP1 whose polarization orientation is tilted by 45°is inserted at a location before the PD1.

There is a phase lead of one wavelength in the phase of the +first-orderlight beams for a displacement corresponding to one pitch of thediffraction grating GS along the x orientation. There is a phase delayof one wavelength in the phase of the -first-order light beams. As theselight beams are reflected by the corner cube prisms and diffracted oncemore at the same order as before, a phase difference for fourwavelengths is added to the phase of the merged light beams when thelight beams are merged at point P1.

As described above, the light beam having a frequency f₁ is expressed asu₁ =a·exp {i (w₁ t)}, and the light beam having a frequency f₂ isexpressed as u₂ =a·exp {i (w₂ t)}. Since, in the above equation, w₁ =2πf₁ and w₂ =2π f₂, the merged light beams form a beat signal with afrequency corresponding to the difference between f₁ and f₂. The phase δcorresponding to the amount of movement x of diffraction grating GS isexpressed as follows with the grating constant of the diffractiongrating GS as p: ##EQU19## Since the phase δ of the diffraction gratingGS is added to the +first-order light beam diffracted at point P1 havinga frequency f₁ each time it is diffracted and the finally +first-orderdiffracted beam is diffracted two times, the following expression can bemade when the light beam is incident on the photoreceptor element PD2:

    u".sub.1 =a"·exp {i (w.sub.1 t+2δ)}.

Since the phase δ of the diffraction grating GS is subtracted from the-first-order light beam diffracted at point P1 having a frequency f₂each time it is diffracted and finally -first-order diffracted beam isdiffracted two times, a light beam expressed as

    u".sub.2 =b"·exp {i (w.sub.2 t=2δ)}

is incident on the photoreceptor element PD2. Therefore, an opticalheterodyne signal obtained by the photoreceptor element PD2 is expressedas follows:

    I.sub.PD2 =a".sup.2 +b".sup.2 +2a"b" cos {(w.sub.1 -w.sub.2) t+4δ}

The frequency of this signal is the same as the difference between f₁and f₂. The phase thereof leads by an amount 4δ proportional to theamount of movement of the diffraction grating GS in comparison with acase before the light beam is made to enter the diffraction grating GS.Since the phase δ of the diffraction grating GS is added to the+first-order light beam, diffracted at point P2, having a frequency f₂each time it is diffracted and the finally +first-order diffracted beamis diffracted two times, the following equation can be made when thelight beam is incident on the photoreceptor element PD1:

    u'".sub.2 =b'" exp {i (w.sub.2 t+2δ)}.

Since the phase δ of the diffraction grating GS is subtracted from the-first-order light beam, diffracted at point P2, having a frequency f₁each time it is diffracted and the finally -first-order diffracted beamis diffracted two times, a light beam expressed as

    u'".sub.1 =a'" exp {i (w.sub.1 t-2δ)}

is incident on the photoreceptor element PD1. Therefore, an opticalheterodyne signal obtained by the photoreceptor element PD1 is expressedas follows:

    I.sub.PD1 =a'".sup.2 +b'".sup.2 +2a'"b'" cos {(w.sub.1 w.sub.2) t-4δ}

The frequency of this signal is also equal to the difference between f₁and f₂. The phase thereof is delayed by an amount 4δ proportional to theamount of movement of the diffraction grating GS in comparison with acase before the light beam is made to enter the diffraction grating GS.The two optical heterodyne signals obtained by the photoreceptorelements PD1 and PD2 are input to the phase difference detector PDC. Thephase difference between the signals is detected by the detector PDC tomeasure the amount of movement of the diffraction grating GS.

If the grating constant of the diffraction grating GS is set at 1.6 μmand the amount of movement of diffraction grating GS is denoted as x,the following relation is satisfied: ##EQU20## Therefore, when a phasedeviation of one cycle, i.e., 8δ=2π [rad], is detected, it is clear thatthe diffraction grating GS is moved by 1.6 μm≈8=0.2 μm. Detection of anamount of movement with a high degree of resolution is made possible bymaking the minimum detection phase difference sufficiently smaller thanone cycle. The use of the phase difference detector capable of resolvingup to 0.2° permits a displacement to 0.11 [nm] to be measuredtheoretically.

Each of the above-described embodiments can be used for a speedmeasuring apparatus which measures speed as an amount of displacementper unit time. According to the above-described embodiments, a measuringapparatus having a higher degree of resolution than before can be usedto detect optical displacement information.

Many different embodiments of the present invention may be constructedwithout departing from the spirit and scope of the present invention. Itshould be understood that the present invention is not limited to thespecific embodiments described in this specification. To the contrary,the present invention is intended to cover various modifications andequivalent arrangements included within the spirit and scope of theclaims. The following claims are to be accorded a broad interpretation,so as to encompass all possible modifications and equivalent structuresand functions.

What is claimed is:
 1. A measuring method comprising the stepsof:forming a first pair of beams and a second pair of beams, each ofsaid first and second pairs of beams having a lower frequency light beamand a higher frequency light beam and each of the first and second pairsof beams being formed so that beat signals therefrom have the samefrequency; changing a phase by causing the lower frequency light beam ofsaid first pair of beams and the higher frequency light beam of saidsecond pair of beams to pass through a predetermined optical path forcausing phases thereof to be shifted in one direction so thatinformation of a shifting phase of light is measured; forming a firstbeat signal of said first pair of beams using the lower frequency lightbeam of said first pair of beams which passed through said predeterminedoptical path; forming a second beat signal of said second pair of beamusing the higher frequency light beam of said second pair of beams whichpassed through said predetermined optical path; andcomparing said firstbeat signal with said second beat signal to measure the information ofthe shifting phase of light.
 2. A measuring method according to claim 1,wherein said predetermined optical path is an optical path on a side ofan interference system at which a length of an optical path of theinterference system is detected, and the information of the shiftingphase of light is measured as the change in the optical length of saidside.
 3. A measuring method according to claim 1, wherein the lowerfrequency light beam of said first pair of beams and the higherfrequency light beam of said second pair of beams pass through adiffraction grating in said predetermined optical path, and theinformation of the shifting phase of light is measured as information ona position of said diffraction grating.
 4. A measuring apparatus,comprising:beam forming means for forming a first pair of beams and asecond pair of beams, each of said first and second pairs of beamshaving two light beams whose frequencies are different and each of saidfirst and second pairs of beams being formed so that beat signals formedtherefrom have the same frequency; optical means for causing a lightbeam of a lower frequency of said first pair of beams and a light beamof a higher frequency of said second pair of beams to pass through apredetermined optical path for shifting the phases thereof in onedirection so that information of a shifting phase of light is measured;first detection means for detecting a first beat signal formed by saidfirst pair of beams, said first beat signal being formed using the lowerfrequency light beam of said first pair of beams which passed throughsaid predetermined optical path; second detection means for detecting asecond beat signal formed by said second pair of beams, said second beatsignal being formed using the higher frequency light beam of said secondpair of beams which passed through said predetermined optical path; andmeasuring means for measuring the information of the shifting phase oflight by comparing said first beat signal with said second beat signal.5. A measuring apparatus according to claim 4, wherein saidpredetermined optical path is an optical path on a side at which alength of an optical path of an interference system is detected, and theinformation of the shifting phase of light is measured as information onthe change in the optical path length of said side.
 6. A measuringapparatus according to claim 4, wherein the lower frequency light beamof said first pair of beams and the higher frequency light beam of saidsecond pair of beams pass through a diffraction grating in saidpredetermined optical path, said optical means causes the higherfrequency light beam of said first pair of beams and the lower frequencylight beam of said second pair of beams to pass through said diffractiongrating through an optical path different from said predeterminedoptical path, and said measuring means measures the information of theshifting phase of light as information on a position of said diffractiongrating.
 7. An apparatus for measuring information on a displacement ora position of an object, comprising:light source means for forming afirst pair of beams and a second pairs of beams, each of said first andsecond pairs of beams having two light beams whose frequencies aredifferent and each of said first and second pairs of beams being formedso that beat signals formed therefrom have the same frequency; opticalmeans for causing a light beam of a lower frequency of said first pairof beams and a light beam of a higher frequency of said second pair ofbeams to enter an object, as a result of which a change in phase beinggiven to the lower frequency light beam of said first pair of beams andthe higher frequency light beam of said second pair of beams isproportional to the displacement or the position of the object in onedirection; first photodetection means for detecting a first beat signalformed using the lower frequency light beam of said first pair of beamswhich passed through the object; second photodetection means fordetecting a second beat signal formed using the higher frequency lightbeam of said second pair of beams which passed through the object; andsignal processing means for measuring information on the position or thedisplacement of said object by comparing said first beat signal withsaid second beat signal.
 8. An apparatus according to claim 7, whereinsaid optical means has a Michelson interferometer that causes the lowerfrequency light beam of said first pair of beams and the higherfrequency light beam of said second pair of beams to pass through amovable mirror as the object and causes a light beam of a higherfrequency of said first pair of beams and a light beam of a lowerfrequency of said second pair of beams to pass through a reference-sidemirror, and said signal processing means measures a displacement alongthe incidence of a light beam of said movable mirror.
 9. An apparatusaccording to claim 7, wherein said optical means causes the lowerfrequency light beam of said first pair of beams and the higherfrequency light beam of said second pair of beams to pass through afirst diffraction grating as said object and to be diffracted at apositive order and causes the higher frequency light beam of said firstpair of beams and the lower frequency light beam of said second pair ofbeams to pass through said first diffraction grating and to bediffracted at a negative order, and further comprising:means forseparating a part of said first and second pair of beams; second opticalmeans for causing a light beam of a lower frequency of said separatedpart of the first pair of beams and a light beam of a higher frequencyof said separated part of the second pair of beams to pass through asecond diffraction grating and to be diffracted at a positive order andcausing a light beam of a higher frequency of said separated part of thefirst pair of beams and a light beam of a lower frequency of saidseparated part of the second pair of beams to pass through said seconddiffraction grating and to be diffracted at a negative order; thirdphotodetection means for detecting a third beat signal formed using saidseparated part of the first pair of beams which passed through saidsecond diffraction grating; and fourth photodetection means fordetecting a fourth beat signal formed using said separated part of thesecond pair of beams which passed through said second diffractiongrating, wherein said signal processing means measures the gratingarrangement orientation positional relation between said first andsecond diffraction gratings on the basis of outputs from said first tofourth photodetection means.